He died of a heart attack, according to his agent, Ornella Cogliolo.
Born in Leningrad in the former Soviet Union, Berman was performing with the Moscow Philharmonic by the time he was 10 years old. The Soviet government did not allow him to perform abroad until the 1970s, so his international career began relatively late in life. His U.S. debut in 1976 was followed by sold-out American tours.
He performed with such ensembles as the New York Philharmonic and the Los Angeles Philharmonic, and with such conductors as Herbert von Karajan, Leonard Bernstein, Daniel Barenboim, and Claudio Abbado.
Among his most famous recordings are Tchaikovsky's Piano Concerto No. 1, performed under von Karajan, and Liszt's Transcendental Etudes.
Berman moved to Italy in the 1990s, and spent the last decade of his life teaching at the Music Conservatory at Imola.
He is survived by his son, Pavel Berman, a violinist, and his wife, Valentina Berman, a pianist.